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| Mutual Inductance Calculation Method of Arbitrarily Positioned Circular Coils with Convex Ring Type Finite Magnetic Shielding in Wireless Power Transfer |
| Lin Zhiyuan1, Li Zhongqi1,2, Hu Changxuan1, Chen Zhongbang1, Huang Shoudao2 |
1. College of Railway Transportation Hunan University of Technology Zhuzhou 412007 China;
2. College of Electrical and Information Engineering Hunan University Changsha 410082 China |
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Abstract In practice, the structure of the wireless power transfer (WPT) system varies for different application scenarios. And the relative position change between the coils of the transmission system will also be caused by the change of mutual inductance. This affects the transmission efficiency. How to quickly and accurately calculated the mutual inductance is a key step in the process of designing and optimizing the structure of WPT systems. Therefore, it is important to study the calculation method of mutual inductance of coils in WPT system under different relative positions. There is no method for mutual inductance calculation of arbitrary positioned circular coils with convex ring type finite magnetic shielding.
This paper established the model for mutual inductance calculation of circular coil with convex ring type finite magnetic shielding in arbitrary position. The spatial boundary vector analysis method is proposed for the exact solution of mutual inductance. This method is solved for the magnetic vector potential in each region by boundary conditions. The space vector coordinate transformation method is utilized. The expression for the calculation of mutual inductance in arbitrary position is obtained by combining Neumann's formula. The validity of the proposed formula is verified by simulations and experiments from four variations of coil relative position vertical offset, horizontal offset, horizontal angular deflection and horizontal offset plus angular deflection.
The calculated results of the proposed formula are compared with the simulated and experimental results as follows: (1) The maximum error of the calculated results with the simulated and experimental results for vertical offset are 2.84% and 2.48%, respectively. (2) The maximum error of the calculated results with the simulated and experimental results for horizontal offset are 1.49% and 2.85%, respectively. (3) The maximum error of the calculated results with the simulated and experimental results for horizontal angular deflection are 3.26% and 2.86%, respectively. 4) The maximum error of the calculated results with the simulated and experimental results for horizontal offset plus angular deflection are 1.84% and 2.47%, respectively.
The calculation model is written Matlab as a program and Ansys Maxwell simulation software under the same equipment for speed comparison. The shortest average time for Ansys Maxwell simulation is 105.636 s, while the longest average time for Matlab program is 0.121 s. Therefore, the proposed calculation method has a significant advantage in calculation speed. The model structure saved 19.6% material compared to the traditional disk type structure under the same parameters. Except for high angle deflection, the mutual inductance can reach 99% of the mutual inductance of the disk type.
In conclusion, the calculated, simulated and experimental values of mutual inductance are in good agreement. The correctness of the proposed calculation method is verified.
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Received: 31 May 2023
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2024, Vol. 39 
